Seminario di probabilità e statistica matematica
Lunedì 15 maggio, ore 16
Aula di Consiglio, Dipartimento di Matematica Guido Castelnuovo
T.G. Kurtz, University of Wisconsin-Madison,
"Stochastic equations for processes built from bounded generators"
Abstract:
The generator for a pure jump process with bounded jump rate is a bounded
operator on the space of measurable functions. For any such process, it
is simple to write a stochastic equation driven by a Poisson random
measure. Uniqueness for both the stochastic equation and the
corresponding martingale problem is immediate, and consequently, the
martingale problem and the stochastic equation are equivalent in the sense
that they uniquely characterize the same process. A variety of Markov
processes, including many interacting particle models, have generators
which are at least formally given by infinite sums of bounded generators.
In considerable generality, we can write stochastic equations that are
equivalent to these generators in the sense that every solution of the
stochastic equation is a solution of the martingale problem and every
solution of the martingale problem determines a weak solution of the
stochastic equation. It follows that uniqueness for one approach is
equivalent to uniqueness for the other.
Tutti gli interessati sono invitati a partecipare. Per informazioni
rivolgersi a piccioni(a)mat.uniroma1.it